Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3

Lesson 3.5Compare Ratio Relationships

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can compare ratios by finding unit rates or using equivalent ratios.

Why This Matters Two friends used the paint shown to create shades of purple paint. Whose mixture contains the most blue paint?

RememberCompare Ratio Relationships

Comparing Ratio Relationships To compare ratios fairly, make one amount the same in both, or find the unit rate (the amount for just 1). Then you can see which ratio is bigger.

  1. Convert each ratio to a unit rate (e.g. price per item or miles per gallon).
  2. Alternatively, scale both ratios to a common term (like a common denominator).
  3. Compare the resulting unit rates to identify the better buy or faster rate

Words: Unit rate (Tasa unitaria)Equivalent ratio (Razón equivalente)Compare (Comparar)Simplify (Simplificar)Common denominator (Denominador común)

  1. 1Circle the letter of the best answer. Show how you know.

    A ratio table for 3:2 gives the points (3, 2) and (6, 4). Which point also lies on the same graph?

    1. A(2, 3)
    2. B(8, 6)
    3. C(9, 6)
    4. D(9, 5)
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    The graph of a set of equivalent ratios always passes through which point?

    1. A(0, 0)
    2. B(0, 1)
    3. C(1, 1)
    4. D(1, 0)
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    On a graph of cups of juice (x) to cups of water (y), the point (4, 10) is plotted. What ratio does that point show?

    1. A4:10
    2. B4:14
    3. C10:4
    4. D14:10
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A ratio graph passes through (2, 5). Which point is NOT on the same line?

    1. A(4, 10)
    2. B(6, 15)
    3. C(8, 20)
    4. D(10, 20)
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    Two pizza shops are running deals. Mario's Pizza sells 2 large pizzas for $18. Sal's Pizza sells 3 large pizzas for $25. A school needs to buy pizza for a class party and wants to get the best deal per pizza. What is Mario's price per pizza?

    1. A$4.50
    2. B$8.33
    3. C$9.00
    4. D$18.00
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  6. 6Circle the letter of the best answer. Show how you know.

    Two pizza shops are running deals. Mario's Pizza sells 2 large pizzas for $18. Sal's Pizza sells 3 large pizzas for $25. A school needs to buy pizza for a class party and wants to get the best deal per pizza. What is Sal's price per pizza?

    1. Aabout $7.50
    2. Babout $8.33
    3. Cabout $9.00
    4. Dabout $12.50
    Show your work

Explain your thinkingThe two recipes use different amounts, so you cannot compare them directly. How did building equivalent ratios let you compare them fairly?

Sentence starter I scaled both ratios to the same amount of ___, then compared the ___; Chef ___'s recipe is more chocolatey because ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3

Lesson 3.5Compare Ratio Relationships

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can compare ratios by finding unit rates or using equivalent ratios.

Why This Matters Two friends used the paint shown to create shades of purple paint. Whose mixture contains the most blue paint?

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each Chef Academy ratio comparison to the correct winner.

    1. Smoothie A: 2 cups fruit for 6 cups water vs. Smoothie B: 3 cups fruit for 8 cups water — more fruity?
    2. Bagels: 4 for $5 vs. 6 for $9 — better price per bagel?
    3. Trail mix: 6 oz nuts to 10 oz oats vs. 9 oz nuts to 15 oz oats — more nutty?
    4. Dressing: 3 tbsp oil to 4 tbsp vinegar vs. 5 tbsp oil to 8 tbsp vinegar — more oily?
    • ASmoothie B (0.375 > 0.333 fruit per cup)
    • B4 for $5 ($1.25 < $1.50 per bagel)
    • CEqual (both simplify to 3:5)
    • D3:4 (equals 6:8, greater than 5:8)
  2. 2Write the name of the correct group on each line.

    Each chef compared two recipes. Sort their conclusions into Correct or Incorrect.

    Groups: Correct Comparison Incorrect Comparison
    • Sauce 5:6 vs. 7:9 — chef says 5:6 is thicker (more tomato)
    • Punch 2 cups juice for 5 cups water vs. 3 for 8 — chef says the 2:5 punch is more juicy
    • Frosting 3:4 sugar-to-butter vs. 5:8 — chef says 3:4 is sweeter
    • Cocoa 3:7 vs. 2:5 — chef says 3:7 is weaker (less cocoa per oz)
    • Tea 4:5 leaves-to-water vs. 5:7 — chef says 5:7 is stronger
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Two pizza shops are running deals. Mario's Pizza sells 2 large pizzas for $18. Sal's Pizza sells 3 large pizzas for $25. A school needs to buy pizza for a class party and wants to get the best deal per pizza. Which shop is the better deal?

    1. AMario's, because $18 is less than $25
    2. BMario's, because 2 is less than 3
    3. CSal's, because $8.33 per pizza is less than $9.00
    4. DThey cost the same
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Chef Academy's snack bar sells 3 mini quiches for $6 or 5 mini quiches for $8. Which is the better deal per quiche?

    1. A3 quiches for $6
    2. B5 quiches for $8
    3. CThey cost the same
    4. DCannot determine
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Two soup recipes use salt. Recipe A uses 4 tsp salt for 10 cups of broth. Recipe B uses 3 tsp salt for 8 cups of broth. Which soup is saltier per cup?

    1. ARecipe B
    2. BThey are equally salty
    3. CCannot determine
    4. DRecipe A
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    Chef Mara's lemon glaze uses 6 oz of lemon juice for 9 cupcakes. Chef Devi's uses 4 oz for 7 cupcakes. Whose glaze has more lemon per cupcake?

    1. AChef Devi
    2. BChef Mara
    3. CSame amount
    4. DCannot determine
    Show your work

Explain your thinkingThe two recipes use different amounts, so you cannot compare them directly. How did building equivalent ratios let you compare them fairly?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help